Question

u ptsBirths are approximately Uniformly distributed between the 52 weeks of the year. They can be saidto follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimalplaces when possible.a. The mean of this distribution isb. The standard deviation isC. The probability that a person will be born at the exact moment that week 18 begins isP(x = 18) =d. The probability that a person will be born between weeks 10 and 43 isP(10 < x < 43) =e. The probability that a person will be born after week 35 isP(x > 35)f. P(x > 18 x < 32) =g. Find the 47th percentile.h. Find the minimum for the upper quarter.

Answer 1

Step 1

A) The mean distribution

`(1+53)/(2)=(54)/(2)=27.0000`

Step 2

B) The standard deviation

`\begin{gathered} SD=\sqrt[]{(1)/(12)*(b-a)^2} \\ SD=\sqrt[]{(1)/(12)(53-1)^2} \\ SD=\text{ }15.0111 \end{gathered}`

Step 3

C)

`P(x=18)=0`

Step 4

D)

Step 6

F)

`P(x>18|x<32)=\text{ }(32-18)/(32-1)=(14)/(31)=0.4516`

Step 7

G)

`\begin{gathered} \text{The 47th percentile}=1\text{ + }(47)/(100)(53-1)_{} \\ =1+0.47(52)=25.44_{}00 \end{gathered}`

Step 8

`\begin{gathered} \text{The minimum for the upper percentile = 1+((}(3)/(4))(53^{}-1) \\ =1+0.75(52) \\ =1+\text{ 39=40}.0000 \end{gathered}`